Co-Adaptive Multi-Task LoRA: Transfer-Aware, Label-Free Control of Domain Participation
Fine-tuning a single low-rank adapter on many domains at once is multi-task learning: the domains must be co-learned, and how they share the adapter decides whether they help or hurt one another. Most efficient fine-tuning pipelines ignore this and train on a fixed, uniform mixture, leaving two coupled questions unanswered: how much should each domain participate, and which domains should be co-trained given that some transfer positively and others interfere? We show that both answers can be read off cheaply and without labels. A forward pass of the current shared adapter over a small unlabeled probe yields, per domain, a competence signal whose level tracks remaining headroom and whose trajectory tracks learning speed; the drift of these probe representations yields a signed cross-domain affinity that predicts pairwise transfer. We fold both into CoDA, a co-adaptive controller that solves a small entropy-regularized quadratic program on the simplex to set each domain's participation -- jointly its loss weight and its share of the sampled data -- rewarding high-headroom, still-learning, mutually synergistic domains and damping interfering ones. The controller is forward-only, adds no trainable parameters, and wraps any multi-task LoRA pipeline. Across five heterogeneous domains and two backbones, CoDA improves the average over uniform mixing, learned mixtures, gradient-surgery multi-task optimizers, and online data selection while using half the data, and lowers cross-domain gradient conflict. We prove that the competence signal tracks domain risk, that the participation program has a unique fixed point reached by a contraction, and that its solution performs transfer-aware water-filling; analysis, ablations, and controls corroborate each claim.